Chaos is a very interesting branch of science. Many closely related discoveries have been found by people with completely different backgrounds. Mathematicians, meteorologists, physicists, biologists, etc. have all made significant contributions. There's a lot out there that can be studied, and not only is much of it interesting to think about, it's also very common for the patterns which emerge to be beautiful to look at.
I'll start out with some relatively simple fractals, which I've spent some time thinking about, and which I've done some programming to look at. You can find that here, on my Sierpinski Gasket page.
I plan to include several other pages, about fractals in general, percolation, chaotic attractors, John Conway's "Life", and some not really chaos related pages about weird patterns of prime numbers. They're not done yet, so for now, here's some other links:
http://speedracer.nmsu.edu/~jholder/ interactive fiction, raytraced pictures, chaos